Specificity measures based on fuzzy set similarity

In this work we propose to define specificity measures on the basis of measures of similarity for fuzzy sets. Specifically, we calculate specificity of a fuzzy set as the similarity between the set and its closest singleton defined on the same domain. Our contribution is completed by the study of the axiomatic relationship between specificity and similarity measures. We also provide several illustrative examples of specificity measures obtained using our approach on the basis of different similarity measures.